Micropores configurational diffusion

In Fig. 9a and 9b the orders of magnitude of the different diffusion coefficients and the activation energy for diffusion are given as a function of pore size [36], For diffusion in micropores (<2 nm in diameter), the diffusivity can vary over several orders of magnitude, depending on the size and nature of the diffusing species and the microporous media. Diffusion in micropores is often referred to as configurational diffusion. 

The third step, migration inside the micropore, is also denoted as intracrystalline zeolite diffusion or configurational diffusion. 

Within micropores, surface forces are dominant and an adsorbed molecule never escapes completely from the force field of the surface. Diffusion within this regime has been called configurational diffusion, intra-crystalline diffusion, micropore diffusion, or simply surface diffusion. The Maxwell-Stefan formulation, which is generally accepted for diffusion in the bulk fluid phase, can be extended to describe surface diffusion by considering the vacant sites to be a (n + l)-th pseudospecies on the surface [38,47,49-52]. Using the Maxwell-Stefan diffusion formulation, the following relationship was obtained for surface diffusion. 

Configurational diffusion in microporous (molecular sieve) membranes wiU be treated separately. Here the driving force must be described in terms of a chemical potential gradient, which is coupled to partial pressure via adsorption isotherms. In cases where several mechanisms operate simultaneously, the problem of additivity arises and in real membrane systems simplifying assumptions have to made. 

Fig. l A typical sandwich-type membrane gas-diffusion separator, a, side view A, B, plastic blocks with F. threaded fittings and G, engraved grooves M, microporous gas-diffusion membrane, b, top view showing position and configuration of a straight channel groove, c, a simplified schematic presentation of the sandwich-type gas-diffusion separator D, donor stream A, acceptor stream M, membrane. 

This value of diffusivity is in the range of configurational diffusion. The carbon particle was assumed to be exposed to a step change in mercury concentration at its external surface at t = 0 (corresponding to the injection location). The calculations indicate that with a 10 pm activated carbon particle, the intraparticle diffusion will be important only when the pore diameter is about 3 A, i.e., the atomic diameter of mercury. Because the micropore size of the activated carbon is generally larger than 3 A, it can be concluded that intraparticle diffusion is unlikely to be the controlling step in the carbon injection process. 

The typical gas transport mechanisms in porous membranes are molecular diffusion and viscous flow, capillary condensation, Knudsen diffusion, surface diffusion, and configurational or micropore-activated diffusion. The contributions of these different mechanisms depend on the properties of both the membrane and the gas under the operating temperature and pressure. Figure 2.3 illustrates schematically the gas transport mechanisms in a single membrane pore. 

Anderson, JL KathawaUa, lA Lindsey, JS, Configurational Effects on Hindered Diffusion in Micropores, AIChE Symposium Series 84, 35, 1988. 

Membranes can also be used as a reactor where catalysts are used frequently. The membrane may physically segregate the catalyst in the reactor, or have the catalyst immobilized in the porous/microporous structure or on the membrane surface. The membrane having the catalyst immobilized in/on it acts almost in the same way as a catalyst particle in a reactor does, except that separation of the product(s) takes place, in addition, through the membrane to the permeate side. All such configurations involve the bulk flow of the reaction mixture along the reactor length while diffusion of the reactants/products takes place generally in a perpendicular direction to/from the porous/microporous catalyst. 

Shape-selective reactions occur by differentiating reactants, products, and/or reaction intermediates according to their shape and size in sterically restricted environments of the pore structures of microporous crystals16. If all of the catalytic sites are located inside a pore that is small enough to accommodate both the reactants and products, the fate of the reactant and the probability of forming the product are determined by molecular size and configuration of the pore as well as by the characteristics of its catalytic center, i.e., only a reactant molecule whose dimension is less than a critical size can enter into the pore and react at the catalytic site. Furthermore, only product molecule that can diffuse out through the pore will appear in the product. 

When the catalyst is immobilized within the pores of an inert membrane (Figure 25.13b), the catalytic and separation functions are engineered in a very compact fashion. In classical reactors, the reaction conversion is often limited by the diffusion of reactants into the pores of the catalyst or catalyst carrier pellets. If the catalyst is inside the pores of the membrane, the combination of the open pore path and transmembrane pressure provides easier access for the reactants to the catalyst. Two contactor configurations—forced-flow mode or opposing reactant mode—can be used with these catalytic membranes, which do not necessarily need to be permselective. It is estimated that a membrane catalyst could be 10 times more active than in the form of pellets, provided that the membrane thickness and porous texture, as well as the quantity and location of the catalyst in the membrane, are adapted to the kinetics of the reaction. For biphasic applications (gas/catalyst), the porous texture of the membrane must favor gas-wall (catalyst) interactions to ensure a maximum contact of the reactant with the catalyst surface. In the case of catalytic consecutive-parallel reaction systems, such as the selective oxidation of hydrocarbons, the gas-gas molecular interactions must be limited because they are nonselective and lead to a total oxidation of reactants and products. For these reasons, small-pore mesoporous or microporous... 

With Pe = 0.5, it has been calculated that under the chosen conditions in all configurations of the reactor section a membrane surface area of approximately 43,000 m is required for microporous and palladium membranes and 3,300 m for Knudsen diffusion membranes. 

Gas-liquid separation in FI hydride generation have also been achieved using dualphase gas-diffusion separators both in a sandwich and tubular configuration. Yamamoto et al.[47] were the first to report on such a system using a tubular PTFE microporous separator (cf. Sec. 5.2.2) in the hydride generation AAS determination of arsenic, achieving a characteristic concentration of 0.06 The system is shown schematically in Fig. 

Diffusion in microporous solids occurs by activated jumps along the pore channels or across cages within the structure. The rate of diffusion over short distances, of the order of the unit cell repeat, is determined by the frequency of re-orientation of molecules into configurations that permit motion, the strength of interaction with the framework, the distance between adsorption sites and the presence of other molecules in the pores. Structural defects, including... 

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